Automatic division of a Bezier curve with a given ratios
Curve Tools addon provides a multi subdivide tool that may help.
Under user preferences make sure Add Curve: Curve Tools addon is enabled.
In the Edit tab of the 3D View side bar there in the Curve Edit panel there is a Multisubdivide button.
It takes as parameters the percentage of curve segment length you want to place cuts at separated by spaces. For your example at $1:3:1$ you'd have five parts with $0.2$ factor so you need two cuts at 0.2 0.8.
Beware this will measure length along the segment curvature, not in a straight line along an orthogonal axis.